How do you simplify the expression cot^2x+1?

Sep 15, 2016

${\csc}^{2} \left(x\right)$

Explanation:

We have: ${\cot}^{2} \left(x\right) + 1$

This expression can be simplfiified by applying one of the Pythagorean identities: $1 + {\cot}^{2} \left(x\right) = {\csc}^{2} \left(x\right)$

$= {\csc}^{2} \left(x\right)$

Jul 19, 2018

${\csc}^{2} x$

Explanation:

Let's say you didn't know the identity: $1 + {\cot}^{2} x = {\csc}^{2} x$
Another approach could be:

${\cot}^{2} x + 1 =$

${\cos}^{2} \frac{x}{\sin} ^ 2 x + {\sin}^{2} \frac{x}{\sin} ^ 2 x =$

$\frac{{\cos}^{2} x + {\sin}^{2} x}{\sin} ^ 2 x =$

$\frac{1}{\sin} ^ 2 x =$

${\csc}^{2} x$